Compute the volume of the solid bounded by the given surfaces. and the three coordinate planes

Question

Compute the volume of the solid bounded by the given surfaces.  and the three coordinate planes

Quizplus · Accepted Answer

The solid is a right triangular pyramid with base vertices at $(6,0,0)$, $(0,8,0)$, and $(0,0,9)$. The height is given by the equation $z=12-2x-4y$. Therefore, the volume is 
\begin{align*}
V &= \frac{1}{3}	imes(	ext{base area})	imes(	ext{height})\
&=\frac{1}{3}	imes\frac{1}{2}	imes 6	imes 8	imes 9	imes (12-2(6)-4(8))\
&= 432.
\end{align*}

Compute the Volume of the Solid Bounded by the Given